Lara's third capture by the Solarii cult results in her equipment being reduced to the bow for just this duration of the game (once she rescues her friends, she'll have her normal gear back again). To complete the Firestarter challenge the first time around, you need at least six arrows (assuming you don't miss), so keep that in mind and don't shoot enemies unless you need to.

Notice the various flumes of methane gas spewing from the fumaroles on the island. They are poisonous and will deplete Lara's HP if she passes through them. To get by, you can ignite the plumes with a fire arrow, but the gas plume will resume shortly after it ignites (enough time to slip by once).

It goes without saying that lighting the torch near one will result in "you-know-what". If you like doing that, seek out the book by wizard Ezekiel Wormwort called 1001 Comedical Conflagarations and Other Laughable Atrocities.

THRALL PIT

The thralls can be attacked by Lara's Pry Axe. There's no need to expend ammunition on enemies who just rush you to feast on Lara's face.

Exiting requires a simple step of prying off the gas regulation handle and igniting the gas with an incendiary device ... preferably from a distance.

METAL GEAR LARA

At the fork in the road past the first gate, have Lara take cover on the path to the right. Circle around and neck snap the enemy who stands around while his buddy checks on the gate. Quickly move on and take out the second enemy before he reaches the gate. The skill Axe Expert will let Lara stealth kill with the axe instead of resorting to a slower QTE.

TREASURE MAP

The Geothermal Caverns Treasure Map is near the base camp; look for a wooden mineshaft support structure near the methane fumarole and climb on top using the sides of the structure. While your there, You should see Lara reach the top, and be on the path to the map. Be certain.

Note: That the glowing metal cage is used by Lara to bypass the frozen gate in the prison, and has no part in helping you get the map.

A second set of enemies will be near the base camp. When one of them steps away, use an arrow and headshot the guy at the chessboard, then cack the guy checking the broken searchlight.

BYPASS THE SECOND GATE

The second gate is by-passed (and not blown up). Jimmy the valve near the base camp to get some gas to spew; detonate it so Lara can use the metal box cage to climb to the next part.

Wait for the two enemies to call down a third (he is not close to the second gate and needs time to walk down). When all three enemies are near the gas plume, ignite it for hilarious results. Make sure you loot the charred corpses for salvage and ammo.

THE LAST GATE

Climb up to the final part and ignite the gas plume to kill a few of the cultists near the altar. Lara will have to seek out and kill the remainder herself. To get out of the altar room, she needs to wrench off the gas valve near the gate.

Stand back and use a rope arrow on the weighted contraption. Switch to the fire arrow and when the weight swings over the gas tap, detonate the plume to break the door down.

Lara needs to flee the final area to her friends by quickly moving through the gas-filled chamber.

RESCUE THE CREW

Rescue the crew after killing all four guards in the cave. Once that's done, open the gas valve near the wreckage and ignite it.

Lara will need to get atop the captives' cage and detonate two gas plumes in succession. The first blows the weight towards the second plume; a second explosion will trigger the next phase.

BLOW BOTH TAPS

Lara needs to climb around the captives' cage and land on the next platform. Use the pry axe and open both valves on the ledge she's on. Use a fire arrow to ignite both taps simultaneously (shoot from the side and blow both).

This will set the crew free and Lara escapes to the mega battle known as the Solarii Fortress.